# Sabine Hossenfelder says time dilation is due to acceleration

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• Epic Mythology
In summary, Sabine Hossenfelder states in the video that time dilation in the twin's paradox is actually differential ageing caused by acceleration. However, looking at the equations for time dilation, it is clear that time dilation is actually caused by velocity, not acceleration. While acceleration is necessary for differential ageing to occur, the amount of differential ageing is directly related to the velocity profiles of the clocks involved, not the acceleration profiles. Therefore, it is not accurate to say that acceleration causes time dilation.
Ibix said:
Yes. In flat spacetime someone has to accelerate for twins to meet twice, but the effect depends on the velocity and how much time is spent at different velocities, not on acceleration. Working in inertial coordinates, the elapsed time for one twin is ##\int\sqrt{1-v^2(t)/c^2}dt##. Do you see any acceleration term in there?

This is a tricky thing that most relativists get but that to a first approximation, no popular physics writers understand. (Dr. Hossenfelder is a relativist and understands this very well.)

Let's say we have two clocks at a particular moment at rest with respect to each other, but one is accelerating. Thus far there is NO experimental evidence that the clocks' rates are different. For example, one can consider muons (whose lifetime is very short if they're at rest) moving in straight lines at high velocities, and compare them with muons moving in circular storage rings at Fermilab and elsewhere at the same velocity, and they have the same observed lifetime, (given by the usual time dilation formula involving the square root of ##1 - (v/c)^2##) even though the ones moving in circles are experiencing gigantic accelerations and the others are not. So acceleration all by itself does not affect clock rates. (The hypothesis that acceleration by itself does not influence the clock rate is called "the clock hypothesis". There is no theoretical basis for it thus far that I am aware of.) So far, so good.

However, it is known that clocks on an upper level of an apartment building run at a tiny bit faster than those on the ground level; the higher you go, the faster the clock rate. This is not due to the gravity, exactly (the gravitational field is nearly the same), but to the gravitational potential, which is in this case the product of ##g## and the height, ##y##, divided by ##c^2##. (For folks who remember some physics, gravitational potential means "gravitational potential energy per kilogram".) Google "gravitational red shift" for more about this. The equation comparing clock rates is this:

##\Delta t_{\text{higher}} = \Delta t_{\text{lower}}(1 + (gy/c^2))##

If this effect were not taken account of by GPS satellites, your phone apps telling you where you were would be very badly incorrect!

Finally, there is a thing called "the equivalence principle": if an elevator is small enough, you cannot distinguish between the effects of being accelerated up at ##g## meters per second squared or being stationary (or moving with constant velocity) in the earth's gravitational field of ##g## meters per second squared. What this means is that during acceleration, a person with an accelerated clock would measure the rate of an clock at a distance of ##y## meters away as running <i>faster</i> than hers, according to the formula above. That is, the factor of ##(1 - (v/c)^{2})## has to be replaced by ##((1 + gy/c^{2})^2 - (v/c)^2)## in the square root, where $y$ is the distance between the accelerated clock and the unaccelerated clock.

This is the cheap solution to the so-called "twin paradox". Say a traveling twin sets out from earth, goes to a distant star, turns around and comes back. There are three periods of acceleration: near the earth going away, turning around, and near the earth to slow down. During periods of steady motion, both the traveler and the stay at home see each other's clock running slow with respect to each other's (they have to; this is a theory of relativity). During the acceleration near the earth, both twins agree that the stay at home twin's clock runs faster than the traveler's, but not appreciably so, because the distance ##y## is not very big. However, during the turnaround, the traveler thinks the earth based twin's clock runs much faster, due to the large value of ##y##. Detailed calculation shows that this rate is precisely what is needed (with the slight increase near the earth) to reconcile the two twins' clocks.

All of this was worked out by the Danish physicist Christian M\o ller in 1943 using general relativity, though he didn't realize (apparently) that the result was exact. A French physicist, Henri Arzèlies, went through it and showed indeed that the resolution was exact. In fact, general relativity is not needed at all: the equivalence principle and gravitational time dilation are all that are required.

Reference: https://www.physicsforums.com/threa...time-dilation-is-due-to-acceleration.1051866/

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IroAppe and Sagittarius A-Star
vanhees71 said:
Yes, and the clock hypothesis has been confirmed by observation for amazing accelerations. I don't know, why you make such a fuss about some pop-sci youtube video...
So are you saying that Sabine's video is wrong?

Epic Mythology said:
So are you saying that Sabine's video is wrong?
Why do you KEEP asking that same question? This is beginning to look like you are just trolling us.

Forget the damn video and study some actual physics.

PhDeezNutz, vanhees71, russ_watters and 4 others
Epic Mythology said:
So are you saying that Sabine's video is wrong?
As @phinds said, this question has already been answered. Her statement is wrong, or at least not clearly right.

It is time to move on. We are a physics education site, not a YouTube video criticism site. So if this thread is intended to help you learn physics then please move on to some of the substantive responses about the physics that you have received but ignored.

vanhees71, russ_watters, Vanadium 50 and 2 others
Epic Mythology said:
So are you saying that Sabine's video is wrong?
As others already mentioned, for example her statement at 18:00 is wrong.

On the other hand, I like her visualization of the reciprocity of time dilation at 09:51 with help of the hyperbolas of equal proper time in the animated Minkowski diagram.

Dale said:
As @phinds said, this question has already been answered. Her statement is wrong, or at least not clearly right.

It is time to move on. We are a physics education site, not a YouTube video criticism site. So if this thread is intended to help you learn physics then please move on to some of the substantive responses about the physics that you have received but ignored.
Thank you Dale. I will likely be reaching out to Sabine and citing this thread, asking her to please correct her errors. I will be citing Dale the physics expert from physicsforums.com if that is OK with you--thank you:
Her statement is wrong, or at least not clearly right. -Dale, physics expert from physicsforums.com

weirdoguy, PeroK and Dale
Epic Mythology said:
So are you saying that Sabine's video is wrong?
Epic Mythology said:
Thank you Dale. I will likely be reaching out to Sabine and citing this thread, asking her to please correct her errors. I will be citing Dale the physics expert from physicsforums.com if that is OK with you--thank you:
What is wrong with you? Seriously?

PhDeezNutz, russ_watters, martinbn and 1 other person
Epic Mythology said:
Thank you Dale. I will likely be reaching out to Sabine and citing this thread, asking her to please correct her errors. I will be citing Dale the physics expert from physicsforums.com if that is OK with you--thank you:
So I guess that is a clear indication that you are not interested in learning physics, just getting a review.

Feel free to cite me. My statements are a matter of public record.

@ all participants, further posts with no physics content will be deleted. Particularly posts only about the video

russ_watters and phinds
Epic Mythology said:
I would like to learn the proper physics for this topic. Please do share.
If it's to learn relativity, the best way is to stop watching Youtube videos, pick up a copy of Taylor and Wheeler and start working through it.

berkeman, PhDeezNutz, phinds and 2 others
Epic Mythology said:
What physics is Sabine getting wrong? What is the best and most constructive way we can offer a correction so she can better help with the greater mission of teaching proper physics? What should have Sabine said in her video.

If your mission is to correct pop sci videos on youtube, you are on a pretty long mission...

PhDeezNutz
Epic Mythology said:
Would it be better to learn physics from a Ph.D. or professor or textbook, or an internet forum where most folks don't share credentials, research publications, or institutions. Please let me know the best way to learn physics,
The best way to learn physics is through a traditional physics course.

A second good approach is with a textbook (Taylor and Wheeler has already been recommended), but for that it is important to discipline yourself to work the practice problems in the textbook, not just read the material. More learning occurs in practice problems than in passive reading.

Online forums, like this one, can only supplement this kind of learning. We cannot replace it nor serve as a substitute.

Research publications are a good place to learn advanced concepts, but not the basics. They assume that the reader has already mastered the textbook material.

PopSci videos and books are actively harmful.

Epic Mythology said:
Might you have a Ph.D.?
I do, as do many of the primary contributors to this forum. I am also a full time physics educator professionally.

Epic Mythology said:
You say that "(Sabine's) statement is wrong, or at least not clearly right." What physics is Sabine getting wrong?
I explained this in detail in my first post to you, which you glossed over in preference for harping on the video. Please take the time now to read my substantive response and ask follow up questions about the physics.

https://www.physicsforums.com/threa...-is-due-to-acceleration.1051866/#post-6877408

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berkeman, PhDeezNutz, PeroK and 1 other person